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BASIC LESSON 3

Lesson Topics
IntegersMultiple Statements on a Line
Long IntegersMOD
BEEPFOR ... NEXT
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Integers and Long Integers

A variable whose name ends with the percent sign "%" is an integer variable. Such a variable must be a whole number between - 32,768 and + 32,767. Examples of integer variables are
N% X% age% P3% prime3% .
A variable whose name ends with "&" is a long-integer variable. A long integer must be a whole number between - 2,147,483,648 and + 2,147,483,647. Examples are
x& M& fudge& .
The ranges for integers and long integers arise from binary arithmetic; in terms of powers of 2,

32,768 = 215,2,147,483,648 = 231 .

Basic will round off an integer variable to the nearest integer. The program

M% = SQR(5)
PRINT "The square root, to the nearest integer, is"; M%
will round off SQR(5) to the nearest integer 2, to produce the output

The square root, to the nearest integer, is 2 .

BEEP

This command causes the computer to emit an annoying beep - it is useful if you want to wake up the user or to make him mad.

Multiple Statements on a Line

Two or more short statements may be placed on the same line by separating the statements with colons. For smoother readability, it is perhaps better if the statements are related in some way.

Examples :

A = B * H: PRINT "The area is"; A
D = 2 * R: C = 3.14 * D: A = 3.14 * R * R
BEEP: PRINT "Your input is incorrect"

MOD

The MOD operation is meant to be used with integers. The evaluation N MOD M gives the remainder when N is divided by M.

Examples :

8 MOD 3 = 2 27 MOD 4 = 3
11 MOD 2 = 1 20 MOD 5 = 0

Observe that M divides evenly into N whenever N MOD M = 0. The following sequence of statements checks whether an integer M divides evenly into another integer N:

INPUT "What is the integer to be divided"; N
INPUT "What is the dividing integer"; M
IF N MOD M = 0 THEN
PRINT M; "divides evenly into"; N
ELSE
PRINT M; "does not divide evenly into"; N
END IF

FOR ... NEXT

Sometimes you want a program to repeat a procedure several or perhaps many times, but with different values for the variables involved. One way of doing this is to use a FOR ... NEXT loop. Let us suppose you want to compute the sum

12 + 22 + 32 + 42 + 52 + 62 + 72 + 82 + 92 + 102 .

A simple program for doing this is as follows:

S = 0
FOR I = 1 TO 10
S = S + I ^ 2
NEXT I
PRINT "The sum is"; S

How does this program work? It starts off by setting S = 0. Then, letting the loop variable I begin at I = 1, it replaces S by the sum S + 12 = 0 + 1 = 1. Next, setting I = 2, it replaces S by the sum S + 22 = 1 + 4 = 5. Next, setting I = 3, it replaces S by the sum S + 32 = 5 + 9 = 14. The program continues until I = 10, when in the 10th step S is replaced by the sum S + 102. The final value of S then will be the sum you want (namely, 385).

If you want just the sum of the even integers from 1 to 10, say

22 + 42 + 62 + 82 + 102 ,

then you modify the program by putting in a STEP condition:

S = 0
FOR I = 2 TO 10 STEP 2
S = S + I ^ 2
NEXT I
PRINT "The sum is"; S

The program starts with I = 2 and proceeds to I = 10 in steps of 2 units; thus it does the calculations only for I = 2, 4, 6, 8, 10. (If a FOR … NEXT loop does not have a step condition, then Basic assumes the step value is + 1.) You can even step backwards (though this is unusual); the statement

FOR J = 20 to 11 STEP -3

instructs Basic to run J through the integers 20, 17, 14, 11.

The starting point and ending point of a loop, as well as the step size, can be variables. The statement

FOR I = M% to N% STEP K

instructs Basic to let I run through all the integers from M% to N% in steps of K units.

In a FOR … NEXT loop, Basic always assumes the loop and step variables are integers; thus it is unnecessary to use the % symbol after these variables.